Related Resources

Geography by the NumbersStaff Member Solves Mystery of Mapping Equations

By DONNA URSCHEL

John Snyder, one of the most important figures in 20th- century cartography,
and John Hessler, a cartographic preservationist in the Library's Geography
and Map Division, share an important trait: a strong mathematical background.

Recently Hessler used his math expertise to preserve and interpret
Snyder's revolutionary discovery of 1977—the mathematical equations
that enable cartographers to take images from satellites and transform
the data into maps. Known as the Space Oblique Mercator Projection
(SOM), the math formulas ushered in a new era of mapping.

Those equations and other Snyder papers and correspondence found a
home in the Geography and Map Division in 1997, shortly after Snyder's
death, when his wife, Jeanne, donated the archives to the Library.
But the materials sat unprocessed and uninventoried until last year,
when James Flatness, head of acquisitions in Geography and Map, suggested
to Hessler, a newcomer to the Library staff, that his math background
could help interpret the Snyder materials.

"As soon as I opened it up, I was so excited by what I was finding.
And since then I have not been able to crawl out of it and probably
won't crawl out of it for years," Hessler said.

Of Snyder's 360 math programs for SOM, Hessler has reconstructed 99
and plans to work on all of them eventually. It's necessary to reconstruct
the programs, because Snyder used the TI-59 Programmable Calculator
from Texas Instruments, an outdated tool in today's world, which stored
the work on magnetic strips. When one loads the strip into the calculator,
it is not clear how various parts of the equations are broken down
in the programming language.

Hessler pored over Snyder's mathematical manuscripts for hints on
how Snyder allocated memory and assigned variables in the programs
and eventually was able to reconstruct the process.

"Now if researchers come to the Library and ask how Snyder actually
did his empirical investigation on the angular distortion of the SOM,
I could actually show them: ‘Here are his programs and techniques that
have come off these strips,'" Hessler said.

In addition to reconstructing the programs, Hessler created a finding
aid for the collection, an inventory that allows a researcher to come
in and see what's contained in the archives. Hessler also placed Snyder's
mathematical notes in order.

Snyder's development of the equations for SOM transformed mapmaking.
"It was a revolution in cartography," said Hessler. "Everything we
do now is from satellite. It increased the accuracy of maps. It allowed
us to build digital elevation models, allowed us to look at things,
like global warming, melting of ice sheets. All of the stuff that comes
from satellite data was open to mapping, and very, very accurate mapping."

From a young age, Snyder had a precocious interest in maps. In 1942,
at age 16, he started to copy into notebooks map projections and other
geographical facts that interested him. But he charted a different
course in college. Instead of majoring in cartography, he received
a degree in chemical engineering from Purdue University, and after
graduate work at the Massachusetts Institute of Technology (MIT), he
pursued a career in the engineering field.

Mapping remained a lifelong interest for Snyder, who wrote two cartographic
history books, published in the 1960s. While he was a chemical engineer
at CIBA-Geigy Corporation in the late 1960s and 1970s, Snyder continued
to expand his knowledge of cartography by studying projections, corresponding
with eminent cartographers and attending conferences.

In 1976, at a conference at Ohio State University titled "The Changing
World of Geodetic Science," Snyder heard Alden Colvocoresses (Colvo)
speak on the challenges of satellite mapping. Several years earlier,
Colvo, the cartographic coordinator for earth satellite mapping at
the United States Geological Survey (USGS), had invented the general
geometry of the SOM projection. At the conference, however, Colvo lamented
that he had not yet found anyone to work out the mathematical blueprint.
Both the USGS and NASA failed to find the analytical solution.

While map projections are typically static images of a stationary
earth, Hessler said Colvo's SOM had to take into account the element
of time and four principal motions: the satellite's scanner sweep across
the earth's surface, the satellite orbit, the earth's rotation and
the earth's orbital drift.

Snyder returned from the conference intrigued by SOM. In April 1977,
he started to work on the math. Four months later, working part-time
and as an amateur, he derived the equations. Soon after, Colvo offered
Snyder a job at USGS and Snyder accepted.

Hessler said the Snyder archives is unique for the Library. "It's
an amazing thing to have in Geography and Maps. It's the only archives
of this type, where we see a cartographer working through the mathematics
of a complex projection in such a profound and detailed way."

Like Snyder, Hessler has a degree in chemical engineering. He graduated
from Villanova and attended Princeton for some graduate work in math.
Hessler's main interest is biogeography, studying species distribution
and the mathematics of distribution. He worked as a contractor at the
Smithsonian's National Museum of Natural History and was hired at the
Library in 2002.

Hessler's work on the Snyder archives is explained in a paper called
"Mapping Time: John Snyder and the Development of the Space Oblique
Mercator Projection." He submitted the paper to the Phillips Society,
a philanthropic organization that supports the collections in the Geography
and Map Division, and to the International Conference on the History
of Cartography at Harvard University in June.